Looking at the map posted earlier I think all Chavez would need is the cooperation of Chile to put his forces in the thick of it.
However Chile would be very foolish to do so as we import tons of fresh vegetables and fruit from them and I'm sure that would end pronto.
BTW, we helped Britain w/ material and transportation during the Falklands war. IIRC C-130 trips to the Ascensions primarily.
But the Brits are much better prepared now though with a battallion sized defense force on the Island I believe, with a flight of typhoons based at Stanley, and (in all probability) with a SSN lurking around the area.
An assault force will have a much tougher time getting to the island and then on it this time around.